We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy driven bubbly flows for a range of Reynolds (Re) and Atwood (At) numbers. We study the probability distribution function of the horizontal and vertical liquid velocity fluctuations and find them to be in quantitative agreement with the experiments. The energy spectrum shows the k −3 scaling at high Re and becomes steeper on reducing the Re. To investigate the spectral transfers in the flow, we derive the scale-by-scale energy budget equation. Our analysis shows that, for scales smaller than the bubble diameter, the net production because of the surface tension and the kinetic energy flux balances viscous dissipation to give the k −3 scaling of the energy spectrum for both low and high At.

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and lend themselves to recursive techniques to enhance the convergence order. The result is a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators of general applicability across a broad range of problems in computational physics. We show the usefulness of this approach by providing examples from hydrodynamics and electrodynamics.

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We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin–Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilise by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than ${\sim}(k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$ , destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth of total interface length in time. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface.

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